Gardening Australia - - CURIOSITIES -

Di­vide any Fi­bonacci num­ber by the one be­fore it and you get an ap­prox­i­ma­tion of the golden ra­tio, 1.6180339887498948420…, a num­ber that con­tin­ues on for­ever with no dis­cernible pat­tern. (This is called an ‘ir­ra­tional num­ber’.) The quo­tient os­cil­lates above and be­low this num­ber as you progress along the se­ries, and the larger the pair of Fi­bonacci num­bers, the closer the ap­prox­i­ma­tion.

So, for ex­am­ple, 55 di­vided by

34 is 1.617647…, an ac­cu­rate rep­re­sen­ta­tion of the golden ra­tio to two or three dec­i­mal places.

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